For diffusion across a capillary wall, Fick’s law can also be expressed as
Equation 17.18
P = capillary permeability by the substance
Co = concentration of the substance outside the
Ci = concentration of the substance inside the capillary
The PS product provides a convenient expression of available capillary surface area because the intrinsic permeability of the capillary is rarely altered much under physiological conditions. However, in pathological conditions, as with a bee sting, capillary permeability may be altered.
In capillaries, diffusion of lipid-insoluble molecules is restricted to water-filled channels or pores. Movement of solute across the capillary endothelium is complex and involves corrections for attractions between solute and solvent molecules, interactions between solute molecules, pore configuration, and charge on the molecules in relation to charge on the endothelial cells. Such solute motion is not simply a matter of random thermal movement of molecules that seemingly run down a concentration gradient. For small molecules, such as water, NaCl, urea, and glucose, the capillary pores offer little restriction to diffusion (i.e., they have a low reflection coefficient; see the section “ ”). Diffusion of these substances is so rapid that the mean concentration gradient across the capillary endothelium is extremely small. The larger the lipid-insoluble molecules are, the more restricted is their diffusion through capillaries. Diffusion eventually becomes minimal when the molecular weight of the molecules exceeds approximately 60,000. With small molecules, the only limitation to net movement across the capillary wall is the rate at which blood flow transports the molecules to the capillary. Transport of these molecules is said to be flow limited.
With flow-limited small molecules, the concentration of the molecule in blood reaches equilibrium with its concentration in interstitial fluid at a location near the origin of the capillary from its parent arteriole. Its concentration falls to negligible levels near the arterial end of the capillary (
Fig.
17.25A ). If the flow is large, the small molecule can still be present at a distant locus downstream in the capillary. A somewhat larger molecule moves farther along the capillary before it reaches an insignificant concentration in blood. Furthermore, the number of still larger molecules that enter the arterial end of the capillary but cannot pass through the capillary pores equals the number that leaves the venous end of the capillary (see
Fig. 17.25A
With large molecules, diffusion across the capillaries becomes the limiting factor (diffusion limited); that is, the permeability of a capillary to a large solute molecule limits its transport across the capillary wall. Diffusion of small lipid-insoluble molecules is so rapid that diffusion limits blood-tissue exchange only when distances between capillaries and parenchymal cells are great (e.g., as in tissue edema or very low capillary density; see
Fig. 17.25B
Movement of lipid-soluble molecules across the capillary wall is not limited to capillary pores (only ≈0.02% of the capillary surface); it also occurs directly through the lipid membranes of the entire capillary endothelium. Consequently, lipid-soluble molecules move rapidly between blood and tissue. The degree of lipid solubility (oil-to-water partition coefficient) provides a good index of the ease of transfer of lipid molecules through the capillary endothelium.
Both O2 and CO2 are lipid soluble, and they readily pass through endothelial cells. Calculations based on (1) the diffusion coefficient for O2, (2) capillary density and diffusion distances, (3) blood flow, and (4) tissue O2 consumption indicate that the O2 supply of normal tissue at rest and during activity is not limited by diffusion or by the number of open capillaries.